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Many epistemologists have responded to the lottery paradox by proposing formal rules according to which high probability defeasibly warrants acceptance. Douven and Williamson ([2006]) present an ingenious argument purporting to show that such rules invariably trivialise, in that they reduce to the claim that a probability of 1 warrants acceptance. Douven and Williamson’s argument does, however, rest upon significant assumptions—among them a relatively strong structural assumption to the effect that the underlying probability space is both finite and uniform. In this article, I will show that...

Many epistemologists have responded to the lottery paradox by proposing formal rules according to which high probability defeasibly warrants acceptance. Douven and Williamson ([2006]) present an ingenious argument purporting to show that such rules invariably trivialise, in that they reduce to the claim that a probability of 1 warrants acceptance. Douven and Williamson’s argument does, however, rest upon significant assumptions—among them a relatively strong structural assumption to the effect that the underlying probability space is both finite and uniform. In this article, I will show that something very like Douven and Williamson’s argument can in fact survive with much weaker structural assumptions—and, in particular, can apply to infinite probability spaces.